Volume of Prisms and Cylinders 8-5 Volume of Prisms and Cylinders Warm Up Problem of the Day Lesson Presentation Course 3

Volume of Prisms and Cylinders Course 3 8-5 Volume of Prisms and Cylinders Warm Up Find the area of each figure described. Use 3.14 for p. 1. a triangle with a base of 6 feet and a height of 3 feet 2. a circle with radius 5 in. 9 ft2 78.5 ft2

Volume of Prisms and Cylinders Course 3 8-5 Volume of Prisms and Cylinders Problem of the Day You are painting identical wooden cubes red and blue. Each cube must have 3 red faces and 3 blue faces. How many cubes can you paint that can be distinguished from one another? only 2

Volume of Prisms and Cylinders Course 3 8-5 Volume of Prisms and Cylinders Learn to find the volume of prisms and cylinders.

Insert Lesson Title Here Course 3 8-5 Volume of Prisms and Cylinders Insert Lesson Title Here Vocabulary cylinder prism

Volume of Prisms and Cylinders Course 3 8-5 Volume of Prisms and Cylinders A cylinder is a three-dimensional figure that has two congruent circular bases. A prism is a three-dimensional figure named for the shape of its bases. The two bases are congruent polygons. All of the other faces are parallelograms.

Volume of Prisms and Cylinders Course 3 8-5 Volume of Prisms and Cylinders Triangular prism Rectangular prism Cylinder Height Height Height Base Base Base

VOLUME OF PRISMS AND CYLINDERS Course 3 8-5 Volume of Prisms and Cylinders VOLUME OF PRISMS AND CYLINDERS Words Numbers Formula Prism: The volume V of a prism is the area of the base B times the height h. Cylinder: The volume of a cylinder is the area of the base B times the height h. B = 2(5) = 10 units2 V = Bh V = 10(3) = 30 units3 B =  (22) V = Bh = 4 units2 = (r2)h V = (4)(6) = 24  75.4 units3

Volume of Prisms and Cylinders Course 3 8-5 Volume of Prisms and Cylinders Area is measured in square units. Volume is measured in cubic units. Remember!

Additional Example 1A: Finding the Volume of Prisms and Cylinders Course 3 8-5 Volume of Prisms and Cylinders Additional Example 1A: Finding the Volume of Prisms and Cylinders Find the volume of each figure to the nearest tenth. Use 3.14 for . a rectangular prism with base 2 cm by 5 cm and height 3 cm B = 2 • 5 = 10 cm2 Area of base V = Bh Volume of a prism = 10 • 3 = 30 cm3

Additional Example 1B: Finding the Volume of Prisms and Cylinders Course 3 8-5 Volume of Prisms and Cylinders Additional Example 1B: Finding the Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. Use 3.14 for . B =  (42) = 16 in2 Area of base 4 in. V = Bh Volume of a cylinder 12 in. = 16 • 12 = 192  602.9 in3

Additional Example 1C: Finding the Volume of Prisms and Cylinders Course 3 8-5 Volume of Prisms and Cylinders Additional Example 1C: Finding the Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. Use 3.14 for . B = • 6 • 5 = 15 ft2 1 2 Area of base 5 ft V = Bh Volume of a prism = 15 • 7 = 105 ft3 7 ft 6 ft

Volume of Prisms and Cylinders Course 3 8-5 Volume of Prisms and Cylinders Check It Out: Example 1A Find the volume of the figure to the nearest tenth. Use 3.14 for . A rectangular prism with base 5 mm by 9 mm and height 6 mm. B = 5 • 9 = 45 mm2 Area of base V = Bh Volume of prism = 45 • 6 = 270 mm3

Volume of Prisms and Cylinders Course 3 8-5 Volume of Prisms and Cylinders Check It Out: Example 1B Find the volume of the figure to the nearest tenth. Use 3.14 for . B =  (82) Area of base 8 cm = 64 cm2 V = Bh Volume of a cylinder 15 cm = (64)(15) = 960  3,014.4 cm3

Volume of Prisms and Cylinders Course 3 8-5 Volume of Prisms and Cylinders Check It Out: Example 1C Find the volume of the figure to the nearest tenth. Use 3.14 for . B = • 12 • 10 1 2 Area of base 10 ft = 60 ft2 V = Bh Volume of a prism 14 ft = 60(14) = 840 ft3 12 ft

Additional Example 2A: Exploring the Effects of Changing Dimensions Course 3 8-5 Volume of Prisms and Cylinders Additional Example 2A: Exploring the Effects of Changing Dimensions A juice box measures 3 in. by 2 in. by 4 in. Explain whether tripling the length, width, or height of the box would triple the amount of juice the box holds. The original box has a volume of 24 in3. You could triple the volume to 72 in3 by tripling any one of the dimensions. So tripling the length, width, or height would triple the amount of juice the box holds.

Additional Example 2B: Exploring the Effects of Changing Dimensions Course 3 8-5 Volume of Prisms and Cylinders Additional Example 2B: Exploring the Effects of Changing Dimensions A juice can has a radius of 2 in. and a height of 5 in. Explain whether tripling the height of the can would have the same effect on the volume as tripling the radius. By tripling the height, you would triple the volume. By tripling the radius, you would increase the volume to nine times the original.

Volume of Prisms and Cylinders Course 3 8-5 Volume of Prisms and Cylinders Check It Out: Example 2A A box measures 5 in. by 3 in. by 7 in. Explain whether tripling the length, width, or height of the box would triple the volume of the box. The original box has a volume of (5)(3)(7) = 105 cm3. V = (15)(3)(7) = 315 cm3 Tripling the length would triple the volume.

Check It Out: Example 2A Continued Course 3 8-5 Volume of Prisms and Cylinders Check It Out: Example 2A Continued The original box has a volume of (5)(3)(7) = 105 cm3. V = (5)(3)(21) = 315 cm3 Tripling the height would triple the volume.

Check It Out: Example 2A Continued Course 3 8-5 Volume of Prisms and Cylinders Check It Out: Example 2A Continued The original box has a volume of (5)(3)(7) = 105 cm3. V = (5)(9)(7) = 315 cm3 Tripling the width would triple the volume.

Volume of Prisms and Cylinders Course 3 8-5 Volume of Prisms and Cylinders Check It Out: Example 2B A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling the radius or height of the cylinder would triple the amount of volume. The original cylinder has a volume of 4 • 3 = 12 cm3. V = 36 • 3 = 108 cm3 By tripling the radius, you would increase the volume nine times.

Check It Out: Example 2B Continued Course 3 8-5 Volume of Prisms and Cylinders Check It Out: Example 2B Continued The original cylinder has a volume of 4 • 3 = 12 cm3. V = 4 • 9 = 36 cm3 Tripling the height would triple the volume.

Additional Example 3: Music Application Course 3 8-5 Volume of Prisms and Cylinders Additional Example 3: Music Application A drum company advertises a snare drum that is 4 inches high and 12 inches in diameter. Estimate the volume of the drum. d = 12, h = 4 d 2 12 2 r = = = 6 V = (r2)h Volume of a cylinder. = (3.14)(6)2 • 4 Use 3.14 for p. = (3.14)(36)(4) = 452.16 ≈ 452 The volume of the drum is approximately 452 in.2

Volume of Prisms and Cylinders Course 3 8-5 Volume of Prisms and Cylinders Check It Out: Example 3 A drum company advertises a bass drum that is 12 inches high and 28 inches in diameter. Estimate the volume of the drum. d = 28, h = 12 d 2 28 2 r = = = 14 V = (r2)h Volume of a cylinder. = (3.14)(14)2 • 12 Use 3.14 for . = (3.14)(196)(12) = 7385.28 ≈ 7,385 The volume of the drum is approximately 7,385 in.2

Volume of Prisms and Cylinders Course 3 8-5 Volume of Prisms and Cylinders Additional Example 4: Finding the Volume of Composite Figures Find the volume of the the barn. Volume of barn Volume of rectangular prism Volume of triangular prism + = V = (40)(50)(15) + (40)(10)(50) 1 2 = 30,000 + 10,000 = 40,000 ft3 The volume is 40,000 ft3.

Volume of Prisms and Cylinders Course 3 8-5 Volume of Prisms and Cylinders Check It Out: Example 4 Find the volume of the house. Volume of house Volume of rectangular prism Volume of triangular prism + = = (8)(3)(4) + (5)(8)(3) 1 2 5 ft = 96 + 60 4 ft V = 156 ft3 8 ft 3 ft

Volume of Prisms and Cylinders Insert Lesson Title Here Course 3 8-5 Volume of Prisms and Cylinders Insert Lesson Title Here Lesson Quiz Find the volume of each figure to the nearest tenth. Use 3.14 for . 10 in. 1. 2. 3. 2 in. 12 in. 12 in. 10.7 in. 15 in. 3 in. 8.5 in. 942 in3 306 in3 160.5 in3 4. Explain whether doubling the radius of the cylinder above will double the volume. No; the volume would be quadrupled because you have to use the square of the radius to find the volume.